3. (20 points) Use the Fourier transform method to find the output ytn) when the input...
Use the Fourier transform to find the output y(n) when the input is x(n) = (.5)nu(n) for the following systems:
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x) = sin(πx)/πx ): h(t) = 8/π sinc(8t/π) where input x(t) of the LTI system is the following continuous-time signal x(t) = cos(t) cos(8t) a) find the Fourier transform of x(t) b) find the Fourier transform of h(t) c) Is this LTI system BIBO stable? Prove d) find the output y(t) of the LTI system
QUESTION 3 (a) If the Fourier transform of (t) is X(c) = 12 (a+2)j@+6) determine the transform for (-21-1). [5 marks] (b) Based on Figure Q3(b), give the expression for signal xt) in unit step function. From your obtained expression, find the Fourier transform of x(). Then compare your answer using the formula of Fourier transform. x() 10 0 Figure Q3(b) [9 marks] 다. For the linear system in Figure Q3(e), when the input voltage is vr(t) = 2sgn(t) V....
Problem 4 (20 points) Given that the Fourier transform of x(t) is find the Fourier transform of the following signals in terms of X(jo) a. y(t)-etx(t 1) b. y(t)-x(-t) x(t-1) c. y(t)tx(t)
P4- Fourier Transform (20 points) For a stable LTIC system with transfer function, h(t), Find the zero-state response if the input x(t)=δ70(t)(The problem shuld be solved using Fourier Transform) h(t) 上一 -27- TO TOE
Problem 3 Use tables of Fourier Transforms and properties to help deter- mine the Fourier transform of (t)t (sint Problem 4 An LTI system has impulse response )2 h(t) = exp(-4t)2(t) For a particular input (t) the output is observed to be y(t) exp(-4t)ult) exp(-5t)ult). Find ()
Using Z-transform, find the output of an LTID system specified by the linear difference equation: | [n+1]+[n] = 2x[n], if the initial conditions are yl- 1] = 1, and the input x[n] = 4-u[n]. (20 points)
1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Transform of u by applying F to the equation and initial condition; denote this function U(w, t). (b) Find u u(z, t) by taking the inverse transform of the U(w, t) you found in part (a).
1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Transform of u by applying F to the equation and...
(24%) Find the Fourier transform of the signals given below: 1) x() 4e U() x(t) = e-3,Cos(12m)U(t) 2) x(t) = 36(1 + 4) + 26(1) + 43(1-5) 3) x[n]=(0.7)"U(n) 4)
(24%) Find the Fourier transform of the signals given below: 1) x() 4e U() x(t) = e-3,Cos(12m)U(t) 2) x(t) = 36(1 + 4) + 26(1) + 43(1-5) 3) x[n]=(0.7)"U(n) 4)
1. (20 points) Fourier Transform and Inverse Transform Problems: (a) Compute the Discrete-time Fourier transform of signal (b) Determine the signal having the following Fourier transform X(w)cos2w.